Ingrown toenail and/or fungal infection?

Hello, last week my daughter, 6 months and female, had what looked like the beginning of an ingrown toenail. This week it appears there is dead skin peeling off around it.

https://ibb.co/27pBMtGz

She does not seem bothered when I squeeze or play with the toe (washed hand right before and after)

She is not on any medicines and has no history of illness.

I'm curious if this is something I should go to the pediatrician with. We've been there alot this season so I don't want to unnecessarily eat up more of their time.

Thanks!